Effect of FCNC mediated Z boson on lepton flavor violating decays

Abstract

We study the three body lepton flavor violating (LFV) decays ${\mu }^{-}\to e^{-}{e}^{+}{e}^{-}$, ${\tau }^{-}\to l_i^{-}{l}_j^{+}{l}_j^{-}$ and the semileptonic decay $\tau \to \mu \varphi$ in the flavor changing neutral current (FCNC) mediated $Z$ boson model. We also calculate the branching ratios for LFV leptonic B decays, $B_{d,s}\to \mu e$, $B_{d,s}\to \tau e$, $B_{d,s}\to \tau \mu$ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on ${\mu }^{-}\to e^{-}{e}^{+}{e}^{-}$ and ${\tau }^{-}\to {\mu }^{-}{\mu }^{+}{\mu }^{-}$. We find that the branching ratios for $\tau \to eee$ and $\tau \to \mu \varphi$ processes could be as large as $\sim \mathcal{O}(10^{-8})$ and $\mathrm{Br}{B}_{d,s}\to \tau \mu ,\tau e)\sim \mathcal{O}(10^{-10})$. For other LFV B decays the branching ratios are found to be too small to be observed in the near future.

Comments: 15 pages, 8 figures, typos corrected, one more section added, version to appear in EPJC